Problem: Simplify the following expression: $q = \dfrac{-9k + 9}{-45k}$ You can assume $k \neq 0$.
Explanation: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $-9k + 9 = - (3\cdot3 \cdot k) + (3\cdot3)$ The denominator can be factored: $-45k = - (3\cdot3\cdot5 \cdot k)$ The greatest common factor of all the terms is $9$ Factoring out $9$ gives us: $q = \dfrac{(9)(-k + 1)}{(9)(-5k)}$ Dividing both the numerator and denominator by $9$ gives: $q = \dfrac{-k + 1}{-5k}$